I did it, guys, I revisited installing and setting up Homeassistant again because I just cannot let it go.
First off, I used a Raspberry Pi instead of trying to do something fringe like running HAOS in a docker container or a Proxmox VM. I did, however, image it onto an SSD so I am not relying on an SD Card.
After letting the system do it's standard setup for about 20 minutes, I could login to the web interface without any issues.